Question

Question 3 (20 points) a) A 70.0 kg-swimmer stands on a 1,000.0 N-diving board which is connected to a large spring. The spring constant of this spring is 10,000.0 N/m. Calculate the vertical displacement of this spring. b) For a fully-submersed object of finite area A and infinitesimal thickness, derive the expression for the pressure acting on an object as a function of depth. Show all steps. c) The pool is refilled by a hose which has a diameter of 6.0 cm and a connected nozzle with a diameter of 3.0 cm. The flow rate of water through the hose is 1.0 L/s. Calculate the velocity of the water in the hose and in the nozzle d) Is the water pressure greater in the hose or the nozzle? Justify your answer and explain.

Answer 1

borot cu o weight of proog burnno 1000 n. total weight 1000 + mg =1000 + 70 x 9.81 W - 1686.7N 기 = 10000 N/m let x be the displacement in veitical ko L 2 20 le 01 기 1686.4 - 10000 0.168 m Cans) - b ) h A CS Scanned with CamScanner

Let 'A' be a clepth mg Area of C7085-sect 3 the area of the object at of 'h' below water sulface Force acting on the area, FE weight of the vertical water colum above it. density, d=m v d vg 1&v=ah F = d Ang P. 1. E. A d Ahg dia of hose, du = 6cm = 0.06 m hose 2 .: Pressure aetingen Fone 21 Area 11 יר A P = hdg of AW ñ di T Лу 0.062 4 = 2.82x10-3 m2 dia of the nozzle, da 3cm = 0.03 m CS Scanned with CamScanner

area of codes -section of nozzle AN - ñ da 2. MX0:03 1032 4- - 7.06x10-9-my? Flow rate ILIS Q = 10-3 m/s we have , AV bose, ） .: velocity of water at VA Q Alt -3 10 2.82x10-3 4 = 0.35m/s (Ans) Velocity of water at nozzle, AN 10-3 7.06 *10-4 51.42 mils Cans) CS Scanned with CamScanner

d) . According to Bernoulli's theorem, P + 2 v? + gh Ch' does not change P + gh = constant Since P Iv2 constant + а P . Pressure reduces when velocity increases. .. Hose will have greater pressure due to less velocity of flowe CSScanned with CamScanner